As is well known, when an electric motor is driven by an external means, so that the motor's rotor is moved sufficiently quickly relative to its stator, the motor will normally act as a generator of electricity. Equivalently, when sufficient current is supplied to a generator, its rotor will normally move relative to its stator, and the generator will act as a motor. In view of that interchangeability of function, the term “electromotive machine” is used for convenience herein, to refer interchangeably to motors and/or generators.
The most well-known construction of electromotive machine comprises a moveable rotor which rotates inside a fixed, substantially cylindrical stator. The term “rotor” is used herein to describe the part of the electromotive machine that is moved, by an electromagnetic field in a motor, or to induce current in a generator. In some electromotive machines, the rotor does not rotate but rather is, for example, translated linearly. The stator is the fixed part of the machine that generates the driving electromagnetic field in a motor, or in which current is induced in a generator. The stator usually comprises a long length of insulated conductor, wound repeatedly to form a “primary winding”. The winding is usually wound onto a ferrous core, for example a laminated steel core (although a ferrous core is not strictly necessary). A plurality of primary windings may be present in the stator.
The term “coil” is used to refer (i) to a conductor arranged in a slotted core, with a leading coil side in a first slot and a trailing coil side in a second slot, or (ii) in the context of a synchronous machine or dc machine, to a conductor arranged around a pole core. The terms “winding” and “windings” are used to refer to a set of coils; the term is often qualified: for example, “phase winding” means all of the coils connected to one phase.
Electromotive machines can be classified in a number of different ways. One way is by the shape of the stator: it may, for example, be planar (in a linear machine), a cylindrical tube or a disk. Linear machines are used in a wide variety of machines, for example in fairground rides, in baggage-handling machines, in urban transport (e.g. monorail) vehicles and in various other launch applications.
Another classification approach is by whether the stator is single or double, that is, whether there is a stator on one side of the rotor or on two opposite sides.
Another way of classifying a machine is by the form of its rotor (this is probably the most common approach to classification). There are essentially two broad classes of rotor: rotors comprising a permanent magnet and rotors comprising conductors. The former are found in synchronous electromotive machines and the later especially in induction electromotive machines. Wound rotors are also commonly found in synchronous machines: turbo-alternators and machines larger than a few kilowatts generally have wound rotors. The rotor (excitation) winding in a synchronous machine is supplied with D.C. current to produce the same sort of field (which is stationary with respect to the rotor) as a permanent magnet array.
Hybrid types of electromotive machines also exist, in which the rotor comprises both a permanent magnet and conductors. Conductors in a rotor themselves take various forms, for example a simple plate, a “squirrel cage” of interconnected bars, or windings of wires (known as secondary windings).
There are two main forms of (primary) windings in use in stators in small and medium-size machines. The first is double-layer windings, which are employed in induction motors and in some motors with permanent magnet excitation; those machines find use in general industrial applications. The second form of windings is concentrated windings, which are in general use only for motors with permanent magnet excitation; those machines are used for both general industrial applications and (notably) in computer hard-disk drives.
A coil 20 for a double layer winding is shown at FIG. 1. The coil 20 comprises an insulated, conductive wire, wound on a ferrous core 30. For ease of illustration, the stator 10 from a linear motor is shown. Ferrous core 30 includes a plurality of slots 40. The first or leading side 20a of the coil 20 occupies the top half of a slot 40a whilst the second side 20b is positioned in the bottom of a slot 40b one coil pitch away from the first side 20a. As successive coils 20 are positioned in the stator 10 in the manner of FIG. 2, the coils 20 at the ends of the stator 10 overlap, forming a quite bulky side region. FIG. 2 illustrates a stator for a four-pole linear motor; the difficulty of winding a linear machine is apparent: the winding has to terminate at each end and either half-filled slots 40c or coil sides 20c over the ends of the machine must be used (in FIG. 2 both techniques are illustrated, with two half empty slots 40c and two coils 20c outside the end of the machine; see FIG. 2(b)).
Coils 120 for a concentrated winding are shown in FIG. 3. The coil 120 again comprises an insulated, conductive wire, wound on a ferrous core 130. Ferrous core 130 includes a plurality of slots 140. The coils 120 are positioned in the slots 140 as shown in FIG. 4, which like FIG. 2 shows a four-pole linear motor. The concentrated windings 120 are each arranged adjacent to a neighbouring winding 120; in contrast with the double-wound case, adjacent coils do not overlap in the concentrated windings. Although other definitions are possible, a stator comprising concentrated windings is defined (as used herein) as a stator comprising a plurality of windings each arranged adjacent to, but not overlapping with, at least one other winding of the plurality.
The advantage of using this form of winding is immediately apparent. First, there is no coil overlap at the sides of the machine, leading to a larger active pole width for a given total machine width. Second, if open slots 140 are used, the coils 120 can be totally preformed and easily inserted in the slots 140, which leads to reduced labour costs. Finally, the winding produces no difficulties at the ends of the machine since all the slots 140 are filled and there are no coil sides around the ends; that latter point is particularly important when a long stator assembly (for, say, a launcher application) is needed, as stator modules that can be butted up to each other can be made.
FIG. 5 illustrates the slot current pattern for two pole pitches produced by a double layer winding (first the winding is shown and then the slot current patterns). The patterns are very approximately sinusoidal and are symmetrical about the zero line. From the symmetry it can be deduced algebraically that only odd harmonic fields can be present. Furthermore, if the slot currents from all the phases are added with the correct phase relationships, a travelling wave is produced. This can be seen qualitatively by drawing the total slot current at progressive times in the cycle, as shown in FIG. 5, where the field moves on by a ¼ of wavelength in space as time progresses by T/4 of a cycle. There are changes in the shape of the field between the two instants in time, which indicates that harmonic travelling fields are present.
A double-layer winding stator can be used with rotors comprising permanent magnets or conductors for induction. The largely sinusoidal nature of the magnetomotive force (mmf) driven by the slot currents is compatible with a good performance.
The behaviour of the concentrated winding is different and much larger harmonic fields are present. FIG. 6, which is drawn for the first two poles of the machine, illustrates the action. The slot current patterns produced are not symmetrical about the zero line, which means it can be deduced algebraically that both odd and even harmonics are present in the waveform. The travelling wave performance is again illustrated by showing patterns at two instants in time. The considerable change in shape between the two instants indicates that large travelling harmonic fields are present, and algebraic analysis confirms that, and shows that (amongst others) two large travelling fields are present. The first is the two-pole field that the winding is designed to produce and the second is a four-pole field travelling in the negative direction.
Analysis of the harmonics will now be described in more detail.
A single general machine winding which consists of a group of coils connected in series is equivalent to a set of windings, each consisting of a sinusoidal distribution of conductors, the distributions being harmonically related in space. The conductor distribution can then be expressed as a Fourier expansion with a zero average term. It can be assumed that the conditions in a machine are largely unaltered if the conductors and the slots are replaced by patches of infinitely thin conductors positioned on a plane iron surface. The patches of conductors are of the same width and placed in the same positions as the slot openings.
If a slot at θs contains Ns conductors and has a slot opening of 2δ then the conductor distribution produced by the slot is given by:
            N      p        =                  1        π            ⁢                        ∫                                    θ              ⁢                                                          ⁢              s                        -            δ                                              θ              ⁢                                                          ⁢              s                        +            δ                          ⁢                              Ns                          2              ⁢                                                          ⁢              δ                                ⁢                      exp            ⁡                          (                                                -                  j                                ⁢                                                                  ⁢                p                ⁢                                                                  ⁢                                  θ                  s                                            )                                ⁢                                          ⁢                      ⅆ            θ                                          N      p        =                  1        π            ⁢                        sin          ⁢                                          ⁢          p          ⁢                                          ⁢          δ                          p          ⁢                                          ⁢          δ                    ⁢              N        s            ⁢              exp        ⁡                  (                                    -              j                        ⁢                                                  ⁢            p            ⁢                                                  ⁢                          θ              s                                )                    
where p is an integer, the harmonic number.
The winding distribution for say the ‘a’ phase of the winding is then given by
      N    pa    =            1      π        ⁢                  sin        ⁢                                  ⁢        p        ⁢                                  ⁢        δ                    p        ⁢                                  ⁢        δ              ⁢                  ∑                  s          =          1                          s          =          S                    ⁢                        N          sa                ⁢                  exp          ⁡                      (                                          -                j                            ⁢                                                          ⁢              p              ⁢                                                          ⁢                              θ                sa                                      )                              
Where there are Nsa conductors from the ‘a’ phase in the general s th slot at θsa.
An example concentrated winding is shown on FIG. 12. If each of the coils has N turns then the ‘a’ phase distribution is:
            N      pa        =                  N        π            ⁢                        sin          ⁢                                          ⁢          p          ⁢                                          ⁢          δ                          p          ⁢                                          ⁢          δ                    ⁢              (                              exp            ⁢                                                  ⁢            j            ⁢                                                  ⁢            θ                    -                      exp            ⁢                                          j                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                p                            3                                      )                        N      pa        =                            2          ⁢                                          ⁢          N                π            ⁢                        sin          ⁢                                          ⁢          p          ⁢                                          ⁢          δ                          p          ⁢                                          ⁢          δ                    ⁢              exp        ⁡                  (                                    -              j                        ⁢                                                  ⁢            π            ⁢                                                  ⁢                          p              /              3                                )                    ⁢              exp        ⁡                  (                      j            ⁢                                                  ⁢                          π              /              2                                )                    ⁢      sin      ⁢                          ⁢      π      ⁢                          ⁢              p        /        3            
This means that Npa is zero for p=3m where m is an integer.
The equivalent expressions for the other two phases ‘b’ and ‘c’ may be found by an origin shift hence if:Npa=Np then:Npb=Npexp(−2πp/3)and:Npc=Npexp(−4πp/3)
The phase conductor distributions may be resolved into equivalent space sequence sets where nf, nb, and nz are the forward backward and zero components respectively. Then:nf=Np/3{exp(j0)+exp(−j2πp/3+j2π/3)+exp(−j4πp/3+j4π/3)}
and it follows that nf=Np for p=1, 4, 7 etc and is zero for all other p.nb=Np/3{exp(j0)+exp(−j2πp/3+j4π/3)+exp(−j4πp/3+j2π/3)}
and it follows that nb=Np for p=2, 5, 8 etc and is zero for all other p.nz=Np/3{exp(j0)+exp(−j2πp/3)+exp(−j4πp/3)}
the sum of the term in the brackets is zero unless p=3m where m is a positive integer. Therefore since it was deduced earlier that Np is zero when p=3m the zero sequence winding distribution is zero for all values of p.
When a positive sequence set of windings is fed with a balanced set of 3 phase currents a positive going field is produced, conversely when a negative sequence set of windings is fed with a balanced set of 3 phase currents a negative going field is produced. It follows that positive going waves are produced at p=1, 4, 7 and negative going waves are produced when p=2, 5, 8
The relative amplitudes of the waves is given by the factor:
            sin      ⁢                          ⁢      p      ⁢                          ⁢      δ              p      ⁢                          ⁢      δ        ⁢  sin  ⁢          ⁢  π  ⁢          ⁢      p    /    3  
The mark to space ratio of the slots and teeth is commonly 60:40, which means thatδ=0.8π/3
for the 3 slot configuration analysed. Taking this value the magnitudes of the waves relative to the wave at p=1 are tabulated in Table 1 below.
A two-pole machine uses 3 coils as shown at FIG. 12(b) and produces a forward-going 2 pole wave and a backward-going 4 pole wave. A four pole machine is given by repeating the 3 coils of the 2 pole machine as shown in FIG. 12(c) and therefore produces a 4 pole forward going wave and a backward going eight pole wave. That has the effect of multiplying p for the 2-pole case by 2, i.e. the (forwards-travelling) fundamental in the 4-pole case corresponds to the (backwards-travelling) second-harmonic in the 2-pole case, with the direction of travel reversed. Therefore the large waves are 4-poles travelling in the positive direction and 8-poles travelling in the negative direction. It will be understood that 2L poles windings can be formed by repeating the 3 coils of FIG. 12(b) L times.
TABLE 1relative magnitude of harmonic waves in the 2-poleand 4-pole cases.p123456789DirectionFBFBFBPole24681012141618numbertwo polewindingPole4812162024283236numberfour polewindingRelative10.66900.070.23300.0780.06840Magnitude
As an illustration of the concentrated windings' action, FIG. 7 shows the addition of a two-pole positively going wave (dashed line) and a four-pole negatively going wave (dotted line). Two instants of time are shown t=0 at FIGS. 7(a), and t=T/4 at 7(b). The total patterns (solid line) approximate in shape to the total slot currents in FIG. 6.
Concentrated windings have been found to be useful only for machines with permanent-magnet rotors, which can produce force only from a field that has the same pole number. That property enables the same concentrated winding to be used with different pole-number secondaries (i.e. rotors), for example, the winding of FIG. 4 could be used with a rotor having either four- or eight-pole permanent magnet arrays.
Attempts have been made to use concentrated windings in induction motors, but the results have been unsatisfactory. The conductors of an induction-motor rotor have been found to respond to and produce force from any harmonic of the stator field; consequently, a large negative force results from the backward going fields produced by concentrated windings, and that detracts from the wanted positive force.
An object of the invention is to provide an electromotive machine, having concentrated primary windings, in which problems associated with prior-art concentrated-primary-winding machines are ameliorated or eliminated.